More Democrats than ever have signed on to a proposal that would shift every U.S. resident onto Medicare, but a large proportion remain uncertain about heading into a completely government-run system as an immediate sequel to Obamacare.

The Medicare for All Act that has been introduced would move everyone in the U.S. onto Medicare, even if they have private healthcare coverage. It is backed by Sen. Bernie Sanders, I-Vt., and an unprecedented 16 Democratic senators. Among them are possible 2020 presidential hopefuls Sens. Cory Booker, D-N.J., Kamala Harris, D-Calif., Elizabeth Warren, D-Mass., and Kirsten Gillibrand, D-N.Y. Most Democratic lawmakers in the House have co-sponsored a similar bill.